Simplify the following expression: $ k = -1 - \dfrac{6r}{7r + 1} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7r + 1}{7r + 1}$ $ \dfrac{-1}{1} \times \dfrac{7r + 1}{7r + 1} = \dfrac{-7r - 1}{7r + 1} $ Therefore $ k = \dfrac{-7r - 1}{7r + 1} - \dfrac{6r}{7r + 1} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-7r - 1 - 6r }{7r + 1} $ Distribute the negative sign: $k = \dfrac{-7r - 1 - 6r}{7r + 1}$ $k = \dfrac{-13r - 1}{7r + 1}$